The Einstein field equation is a non-linear, tensorial, second ordered partial differential equation which is very difficult to solve. The seek for exact solution under special cases with symmetry condition have been preformed throughout the decades. For example, the famous Schwarzschild solution for a black hole [1]}, and numerous fruitful solutions to different cases of vacuum Einstein field equation, for which the stress-energy tensor \(T_{\mu \nu } =0\) . This includes, for instance, Reissner–Nordström electrovacuum, Kerr–Newman electrovacuum, Melvin electrovacuum, Weyl–Maxwell electrovacuum, Bertotti–Robinson electrovacuum and so on [2]}, [3]}.
